PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
80012^218680-71965830Yves Minet05/2012
800218^52424+1765807Lelio R Paula08/2013
800319062^2827+2827^1906265790Hans Havermann08/2019
8004(2*15683^15683+1)/73238442565789David Broadhurst09/2010
8005(23*2^218517+1)/1900365778Lelio R Paula07/2012
8006(5*10^65773+1)/365774Erik Branger12/2013
8007160^29839-15965769Norbert Schneider12/2018
80082^218457-1732965763Enzo Doria05/2013
8009151703#+22338165759Nicolas PALAU10/2016
80102^218436+4075565756Lelio R Paula10/2011
80112^218399-462765745Yves Minet05/2019
8012(F(44)^7433-F(43)^7433)/F(42)65744Wayne Halsdorf03/2012
801315952^13219+13219^1595265742Hans Havermann08/2019
8014157^29934+29934^15765733Serge Batalov05/2014
8015211^28273-265715Lelio R Paula09/2013
8016(59*10^65712+31)/965713Robert Price09/2015
8017611^23586+23586^61165712Norbert Schneider08/2016
8018p(13991)#/2+3265712Robert Price12/2016
801915865^13864+13864^1586565712Hans Havermann07/2019
80202^218282-1848565710Enzo Doria05/2013
80212^218274-11125165708Enzo Doria05/2014
80222*F(314335)-165693Henri Lifchitz12/2009
80232^218200+42765685Henri Lifchitz01/2005
8024(10199^16384+10197^16384)/265676Jeppe Stig Nielsen04/2018
8025(10199^(2^14)+(10197)^(2^14))/265676Robert Price05/2018
802646532!3+365667Robert Price10/2014
80272^218120-14765661Lelio R Paula08/2011
8028452^24729+24729^45265659Norbert Schneider09/2016
80295817^17440+17440^581765657Norbert Schneider06/2019
80302^218102-11489365656Enzo Doria05/2015
8031(15*2^218083-1)/1765650Lelio R Paula01/2014
8032(15*2^218081+1)/1894165646Lelio R Paula08/2012
803315818^14115+14115^1581865640Hans Havermann08/2019
8034(306^26407-1)/30565638Eric Chen09/2017
803519^51326+3665634Lelio R Paula08/2013
8036(21*2^218045-1)/45158365634Lelio R Paula01/2014
80372^217989-3365622Lelio R Paula08/2011
8038(13*2^217961+1)/365614Lelio R Paula06/2012
80394*6^84315-565611Lelio R Paula09/2014
8040(315047^11933+1)/31504865607Faysal YAtim06/2008
80416^84303+5565601Lelio R Paula07/2013
804216585^9024+9024^1658565601Hans Havermann08/2019
804318462^3575+3575^1846265601Hans Havermann08/2019
804415963^12862+12862^1596365597Hans Havermann08/2019
8045(-lucasV(1,2,435857)+2)/(173*859*8017)65595Mike Oakes04/2017
8046(9787*2^217873-1)/3765589Lelio R Paula04/2015
80475*2^217858+365583Lelio R Paula04/2014
8048(19*10^65572+119)/365573Robert Price02/2017
805020^50399+5165571Lelio R Paula08/2013
80497162^17009+17009^716265571Norbert Schneider07/2018
805111^62946-567065552Enzo Doria01/2013
80522^217742-391165547Yves Minet08/2009
8053(19*10^65545+77)/365546Robert Price08/2016
80542^217731+13165544Lelio R Paula08/2011
80552^217720-11128765541Enzo Doria05/2014
8056(365^25579+1)/36665539Eric Chen10/2017
805710^65537+2765538Robert Price01/2011
805810^65537-7685965537Patrick De Geest05/2013
8059(28*10^65532+359)/965533Robert Price11/2017
8060(10223*2^217676+1)/365531Lelio R Paula06/2014
8061PadovanNumber[536485]65518Eric W. Weisstein05/2009
80625*10^65509+2365510Robert Price11/2017
8063(8*10^65507-83)/365508Robert Price10/2017
80647*10^65492-4765493Robert Price02/2017
80652^217547-186840765489Enzo Doria04/2016
80662^217531-11176965484Enzo Doria05/2014
80677^77484-1865482Lelio R Paula06/2013
80685754^17413+17413^575465473Norbert Schneider05/2019
80692^217488-11328565471Enzo Doria07/2014
8070151153#/30-3065468Henri Lifchitz12/2011
80712^217466+425765464Lelio R Paula10/2011
807246396!3-8165455Robert Price09/2014
80732^217421-11318565451Enzo Doria07/2014
8074(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
80752^217408-214565447Lelio R Paula10/2011
80762^217398-1694765444Enzo Doria05/2013
807716097^11628+11628^1609765443Hans Havermann07/2019
80788*5^93613+365434Lelio R Paula09/2014
807915929^12810+12810^1592965430Hans Havermann07/2019
808011^62828-531065429Enzo Doria01/2013
808110^65426+1365427Robert Price01/2011
80822^217341-655565427Lelio R Paula10/2011
808310^65426-5484965426Patrick De Geest05/2013
8084(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
808530011^14608-10865405Enzo Doria07/2012
8086119^31504-265389Lelio R Paula10/2017
8087(43^40031-1)/4265388Robert Price04/2014
80882^217190+9439565381Henri Lifchitz02/2005
808915^55587+4665376Lelio R Paula08/2013
809018443^3502+3502^1844365368Hans Havermann07/2019
80912^217088-11183365350Enzo Doria05/2014
8092(13*2^217069-1)/168294565340Lelio R Paula01/2014
8093(10^65340+47)/365340Robert Price11/2017
8094(62*10^65331+1)/965332Serge Batalov11/2010
80952^216947-11135165308Enzo Doria05/2014
8096-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
8097(13*10^65297+83)/365298Robert Price09/2016
809816413^9502+9502^1641365288Hans Havermann07/2019
80995^93400-865284Lelio R Paula06/2013
81002^216802-16565264Lelio R Paula08/2011
81012^216799-2863565264Lelio R Paula10/2011
81025*10^65255+5165256Robert Price01/2017
81032^216762-16765252Lelio R Paula08/2011
810411^62657-579065251Enzo Doria01/2013
81053^136756-11288065250Enzo Doria06/2014
81062^216752+2165249Lelio R Paula08/2011
81073*10^65247+1165248Robert Price11/2017
810811^62651-270065245Enzo Doria12/2012
810915130^15609-15609^1513065244Norbert Schneider07/2018
8110Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
8111gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
8112(2^216676-1017)/63765224Lelio R Paula04/2012
81132^216652-232765219Yves Minet10/2013
8114(9179*2^216648-1)/466765218Lelio R Paula04/2015
8115(5*10^65203-119)/365204Robert Price04/2016
811615977^12034+12034^1597765193Hans Havermann07/2019
81172^216555-11326965190Enzo Doria07/2014
8119(9513^16384+1)/265181Henri Lifchitz02/2007
811815753^13730+13730^1575365181Hans Havermann07/2019
81202^216474+1291565166Lelio R Paula02/2013
812119^50958-3265163Lelio R Paula08/2013
81222^216442-11213365156Enzo Doria06/2014
81232^216437-11221365155Enzo Doria06/2014
81242^216435-11276765154Enzo Doria06/2014
81252^216420+1270565149Lelio R Paula02/2013
81268*3^136507-765132Lelio R Paula04/2014
8127(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
812816803^7496+7496^1680365109Hans Havermann07/2019
812915132^15575-15575^1513265102Norbert Schneider07/2018
81305*10^65086-5165087Robert Price10/2017
81312^216197-11176965082Enzo Doria05/2014
81326^83631-7965078Lelio R Paula07/2013
8133572^23601+23601^57265078Norbert Schneider08/2016
8135(3^136399-7)/54422065074Lelio R Paula04/2012
813415592^14911+14911^1559265074Hans Havermann07/2019
81362^216154-142165069Yves Minet01/2013
81372^216145-11266365067Enzo Doria06/2014
8138(7*10^65064+53)/365065Robert Price10/2017
8139132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
8140132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
8141148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
8142194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
8143223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
814682090*10^65050+2^216091-165055Gilbert Mozzo07/2012
814595133*10^65050+2^216091-165055Gilbert Mozzo12/2013
814498142*10^65050+2^216091-165055Gilbert Mozzo12/2013
8147((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
81485977*10^65050+2^216091-165054Gilbert Mozzo03/2012
81497*2^216091+2^298-1365051Peter Lesala03/2007
81502^216091+2*29208-165050Makoto Morimoto10/2013
815115845^12736+12736^1584565045Hans Havermann07/2019
8152(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
8153p(13861)#/2+25665039Robert Price05/2017
8154(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
815511^62439-438065024Enzo Doria01/2013
815616489^8776+8776^1648965022Hans Havermann07/2019
81573^136244+265005Mike Oakes11/2009
815813^58343-5064991Lelio R Paula07/2013
8159331^25791-1000264989Enzo Doria07/2012
81602^215877+13164986Lelio R Paula08/2011
81614*5^92959+964977Lelio R Paula09/2014
81622^215789-1882564959Lelio R Paula09/2011
8163(2^215801-509203)/4132764958Lelio R Paula05/2012
8164U(315311)64954Serge Batalov03/2015
816546072!3-5904964951Robert Price12/2015
81662^215750-595564948Lelio R Paula09/2011
816713^58281+4664922Lelio R Paula07/2013
816815633^14212+14212^1563364919Hans Havermann07/2019
81692^215623+18364909Lelio R Paula08/2011
8170(46*10^64904+521)/964905Robert Price08/2017
8171(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
81725*2^215554+364889Lelio R Paula04/2014
81732^215541-11207564885Enzo Doria06/2014
81742*10^64882-364883Dmitry Domanov11/2010
817516592^8121+8121^1659264869Hans Havermann07/2019
817610^64862+34233964863Patrick De Geest05/2013
817710^64862-4764862Robert Price05/2011
817819^50718-8464856Lelio R Paula08/2013
8179(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
818086413!6-1264846Robert Price08/2018
818110^64843+427869783964844Robert Price05/2015
818210^64843+2196764844Patrick De Geest03/2016
818310^64843-34007364843Patrick De Geest03/2016
818411^62254+7064831Lelio R Paula07/2013
81852^215351-11192564828Enzo Doria05/2014
81862^215310-11764815Lelio R Paula08/2011
8187124^30958-12364809Norbert Schneider02/2015
8188(7*10^64807+17)/364808Erik Branger03/2014
8189(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
81902^215243-1594964795Enzo Doria04/2013
819123^47581-22^4758164793Robert Price08/2012
8192(62*10^64783-17)/964784Robert Price09/2015
81935*3^135747-464769Lelio R Paula04/2014
8194(59*10^64767-41)/964768Robert Price09/2015
8196(2^215140+3)/1964763Lelio R Paula04/2012
81952^215135-1716964763Enzo Doria05/2013
819716078^10665+10665^1607864762Hans Havermann07/2019
81982^215115-11127764757Enzo Doria05/2014
81999*5^92641+264755Lelio R Paula09/2014
8200(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
82015791^17200+17200^579164720Norbert Schneider12/2018
8202(5*10^64715-23)/964715Robert Price11/2014
82032^214938-178164703Yves Minet03/2013
820421003^1202+1202^2100364688Hans Havermann07/2019
820511^62111-42064682Enzo Doria08/2012
820618870^2677+2677^1887064680Hans Havermann07/2019
82075^92525+4264673Lelio R Paula06/2013
82082^214824+7189364669Enzo Doria04/2016
820919157^2374+2374^1915764665Hans Havermann08/2019
82102^214799-222164661Yves Minet08/2013
821118393^3274+3274^1839364653Hans Havermann07/2019
82125939^17128+17128^593964637Norbert Schneider10/2018
8213(21*2^214688+1)/29364627Lelio R Paula08/2012
821492^32907+32907^9264623Serge Batalov05/2014
821517650^4579+4579^1765064613Hans Havermann07/2019
8216(89*10^64608-539)/964609Robert Price11/2017
82176^83013+10164597Lelio R Paula07/2013
8218p(13775)#/2+864594Robert Price01/2017
8219(7*10^64568-43)/964568Robert Price10/2014
8220Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
8221(24737*2^214476+1)/287764565Lelio R Paula06/2014
8222(47*2^214463+1)/764561Lelio R Paula04/2015
82232^214458+5461564559Lelio R Paula10/2011
8224(3^135322+7)/12291140864557Lelio R Paula04/2012
82252^214389-68311364538Paul Bourdelais03/2013
8226(76*10^64534+113)/964535Robert Price11/2017
82272^214369-11124164532Enzo Doria05/2014
8228(19^50461+3^50461)/2264526Robert Price07/2013
822911^61954-366064519Enzo Doria12/2012
8230(23*2^214319-1)/2164517Lelio R Paula01/2014
8231(58695*2^214310-1)/57164516Lelio R Paula04/2015
82322^214300-454764511Yves Minet03/2019
823335^41779-3464510Norbert Schneider04/2014
8234(159^29303+1)/16064506Eric Chen12/2017
8235(89*10^64504-179)/964505Robert Price11/2017
823611^61939-522064503Enzo Doria01/2013
8237(2^214271+78557)/3564501Lelio R Paula05/2012
8238L(308604)+P(308604)64495Robert Price12/2017
8239126^30706-12564494Norbert Schneider02/2015
8240gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
82412^214215+1290964486Lelio R Paula10/2011
824216581^7738+7738^1658164478Hans Havermann07/2019
82435^92225+6664463Lelio R Paula06/2013
82442^214126-24055164459Paul Bourdelais03/2013
82458*6^82827+564453Lelio R Paula09/2014
8246(31*2^214120-1)/217048564452Lelio R Paula01/2014
8247(31*2^214088-1)/595564445Lelio R Paula01/2014
824814^56227+8964444Lelio R Paula08/2013
824910^64436+266764437Patrick De Geest05/2013
825065^35543-64^3554364437Robert Price08/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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